Question

If a rectangle and a parallelogram have an equal base and the same perimeter, then the area of the rectangle will be ______ area of the parallelogram.

• A. Equal to
• B. Greater than
• C. Less than
• D. None

Answer 1

Answer: (B)

Greater than

Let length and breadth of rectangle be $b$ and $a$ respectively.

Then, area of rectangle $=a\times b$

Also, area of IIgm $=b\times h$

Also, $sin\alpha =\frac{h}{a}\Rightarrow h=a\sin \alpha$

Hence, area of IIgm $=ab\sin \alpha$

$\alpha <{90}^0,so,\sin \alpha <1\Rightarrow ab\sin \alpha <ab$

Hence, area of IIgm < rectangle area

or area of rectangle > area of IIgm.